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Re: Maximum Cardinality of an RDF Model

From: Jon Awbrey <jawbrey@oakland.edu>
Date: Mon, 22 Jan 2001 10:42:48 -0500
Message-ID: <3A6C54F8.6381C76C@oakland.edu>
To: Miles Sabin <MSabin@interx.com>
CC: RDF Logic <www-rdf-logic@w3.org>
Miles Sabin wrote:
> 
> Working on the assumption that there's at most a countably
> infinite set of URI(-refs) ... each is a finite sequence of
> charaters drawn from a finite alphabet ... and similarly for
> Literals, am I right to infer that,
> 
> 1. there is at most a countable infinity of resources: because
>    every resource has a URI(-ref) and no two distinct resources
>    share a URI(-ref).
>
> hence that,
> 
> 2. the set Resources from rdfms 5.1, is at most countably
>    infinite,
> 
> 3. the set Properties from 5.3 is at most countably infinite:
>    because a (proper) subset of Resources.
> 
> and hence that,
> 
> 4. RDF models can contain at most countably many statements:
>    becauce they're subsets of,
> 
>    Properties x Resources x (Resources U Literals)
> 
>    which is at most countably infinite because Properties,
>    Resources and Literals are.
> 
> Cheers,
> 
> Miles
> 
> --
> Miles Sabin                               InterX
> Internet Systems Architect                5/6 Glenthorne Mews
> +44 (0)20 8817 4030                       London, W6 0LJ, England
> msabin@interx.com                         http://www.interx.com/

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Miles,

Here's the rub:

Do you want to talk about real resources, the resources that there are,
or do you want to talk about resources for which you have proper names?

This is where it all begins, the formal linguistic aspect of this
science of computation of ours, way back with Wilhelm von Humboldt,
and the requirement that we "make infinite use of finite means".
The catch is known as the "instrumental pigeonhole principle",
saying that if there are large cardinalities of resources
but only small cardinalities of proper names, then some
of the names that we just called proper are really not,
but refer more properly to "generals".  And if you
try to be a "nominal thinker", and try as you are
charged "not to confuse a general name with the
name of a general", then you are bound to go
through your "life of computation" (LOC),
hopelessly confused.

Many Regards,

Jon Awbrey

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Received on Monday, 22 January 2001 10:42:35 GMT

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